Bring a medium pot of water to a boil. Add the beets and cook until very tender, about 1 hour.

Drain and peel the beets, discarding the cooking liquid, then transfer to a blender along with the tahini, lemon juice, garlic, and ice cubes. Season with salt and pepper and puree until very smooth. Spoon into a shallow serving bowl, drizzle with olive oil, garnish with pine nuts, and serve with Egyptian flatbread or pita, for scooping.